Preheat the oven to 400 degrees F (200 degrees C).

Cook bacon in a large skillet over medium heat until evenly brown and crisp. Drain on paper towels, crumble, and set aside.

Heat olive oil in a large skillet over medium-high heat. Add onion; cook and stir until translucent. Reduce heat to medium and add portobello mushrooms. Continue cooking until mushrooms are tender. Remove the skillet from heat and set aside.

Bring a saucepan of salted water to a boil over high heat. Cook asparagus in boiling water until just tender, 1 to 2 minutes. Immediately drain and run under cold water to cool. Set aside.

Brush pie shell with beaten egg white. Place onion-mushroom mixture, asparagus, and crumbled bacon into the bottom of pie shell. Sprinkle with Cheddar and feta cheese.

Whisk together eggs, cream, salt, and pepper in a medium bowl until smooth. Pour over vegetable-cheese filling in pie shell.